Magnetic position sensors, systems and methods

ABSTRACT

Magnetic position sensors, systems and methods are disclosed. In an embodiment, a position sensing system includes a magnetic field source; and a sensor module spaced apart from the magnetic field source, at least one of the magnetic field source or the sensor module configured to move relative to the other along a path, the sensor module configured to determine a position of the magnetic field source relative to the sensor module from a nonlinear function of a ratio of a first component of a magnetic field of the magnetic field source to a second component of the magnetic field of the magnetic field source.

RELATED APPLICATION

This application is a divisional of application Ser. No. 13/213,338filed Aug. 19, 2011, which is hereby fully incorporated herein byreference.

TECHNICAL FIELD

The invention relates generally to sensors and more particularly tomagnetic position sensors.

BACKGROUND

Magnetic sensors can be used for linear position sensing, i.e., sensingthe position of a target in one dimension, as well as multi-dimensionalpositioning sensing. A permanent magnet is attached to the target, andthe magnetic field of the magnet is measured by the magnetic sensor.

Conventional solutions for position sensing using magnetic sensorssuffer from drawbacks, however. Some solutions do not have thecapability to sense position in multiple dimensions. Others are notaccurate and/or require mathematically complex calculations that aredifficult to carry out with limited silicon area.

Therefore, there is a need for improved magnetic position sensors,sensing systems and methods.

SUMMARY

Magnetic position sensors, systems and methods are disclosed.

In an embodiment, a position sensing system comprises a magnetic fieldsource; and a sensor module spaced apart from the magnetic field source,at least one of the magnetic field source or the sensor moduleconfigured to move relative to the other along a path, the sensor moduleconfigured to determine a position of the magnetic field source relativeto the sensor module from a nonlinear function of a ratio of a firstcomponent of a magnetic field of the magnetic field source to a secondcomponent of the magnetic field of the magnetic field source.

In an embodiment, a method of sensing a linear position of an objectcomprises coupling one of a permanent magnet or a sensor to the object,the permanent magnet being magnetized in a z-direction; arranging theother of the sensor or the permanent magnet proximate to and spacedapart from the one of the permanent magnet or the sensor in ay-direction; sensing a change in an x-direction of a magnetic fieldcomponent Bz of the permanent magnet by a first sensor element of thesensor; sensing a change in the y-direction of the magnetic fieldcomponent Bz of the permanent magnet by a second sensor element of thesensor; determining a ratio of dBz/dx to dBz/dy; and determining aposition of the object on the path from the ratio.

In an embodiment, a method of sensing a linear position of an objectcomprises coupling one of a permanent magnet or a sensor to the object,the permanent magnet being magnetized in a y-direction; arranging theother of the a sensor or the permanent magnet proximate to and spacedapart from the one of the permanent magnet or the sensor in ay-direction and a z-direction; sensing a Bx component of a magneticfield of the permanent magnet by a first sensor element of the sensor;sensing a Bz component of the magnetic field of the permanent magnet bya second sensor element of the sensor; determining a nonlinear functionof Bx and Bz; and determining a position of the object on the path fromthe nonlinear function.

In an embodiment, a position sensing system comprises a dipole magnethomogenously magnetized in a z-direction and having a vanishing octupolemoment; and a sensor module positioned proximate to but spaced apartfrom the dipole magnet and comprising a plurality of sensor elements tosense x, y and z components of a magnetic field of the dipole magnet,the sensor module configured to determine a relative position of themagnet to the sensor module from the x, y and z components of themagnetic field.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be more completely understood in consideration of thefollowing detailed description of various embodiments of the inventionin connection with the accompanying drawings, in which:

FIG. 1 is a block diagram of a magnet and sensor according to anembodiment.

FIG. 2 is a diagram of a magnet path according to an embodiment.

FIG. 3A is a graph of magnetic field components versus distanceaccording to an embodiment.

FIG. 3B is a graph of a ratio of magnetic field components versusdistance according to an embodiment.

FIG. 3C is a graph of distance error versus distance according to anembodiment.

FIG. 4A is a diagram of a sensor system according to an embodiment.

FIG. 4B is a diagram of a sensor system according to an embodiment.

FIG. 5A is a graph of magnetic field gradients versus distance accordingto an embodiment.

FIG. 5B is a graph of distance error versus distance according to anembodiment.

FIG. 6A is a block diagram of a sensor system according to anembodiment.

FIG. 6B is a block diagram of a sensor system according to anembodiment.

FIG. 7A is a diagram of a sensor system according to an embodiment.

FIG. 7B is a diagram of a sensor system according to an embodiment.

FIG. 7C is a diagram of a sensor system according to an embodiment.

While the invention is amenable to various modifications and alternativeforms, specifics thereof have been shown by way of example in thedrawings and will be described in detail. It should be understood,however, that the intention is not to limit the invention to theparticular embodiments described. On the contrary, the intention is tocover all modifications, equivalents, and alternatives falling withinthe spirit and scope of the invention as defined by the appended claims.

DETAILED DESCRIPTION

Embodiments relate to magnetic position sensors.

FIG. 1 depicts a magnet 100 and a sensor system 102 configured to sensea position of the magnet. Magnet 100 is, most generally, a source ofmagnetic field and can comprise a permanent magnetic, electromagnet,coil winding or some other configuration in embodiments. As oriented inFIG. 1, the magnet is magnetized in the vertical (z) direction, andsensor system 102 senses a linear position of magnet 100 on the x-axis,but these orientations and axes can vary in other embodiments. Theparticular axes, coordinate systems and orientations used hereinthroughout are used for illustration and convenience only and are notfixed in space. Rather, x-, y- and z-axes are used to describe threeperpendicular axes of an axis system that can be oriented in any spacedirection and can be stationary, moving and/or rotating relative toEarth's coordinate system.

Sensor system 102 detects the By and Bz components, where y is thecoordinate along the magnet path and z is the vertical direction.Conventional systems estimate the y-position according to the following:

Xpos=m*arctan(By/Bz)

These calculations are complex, and the system works only if sensorsystem 102 is directly below the path without any y-shift and at awell-defined vertical distance. Even then, the equation is only anapproximation. Additionally, the results are linear only within aparticular range of x. Thus, the results are not precise and arecomputationally complex to obtain.

Embodiments utilize similar magnet-sensor configurations but makecertain assumptions that improve the accuracy and reduce the complexityof the system. Referring to FIG. 2, sensor system 102 is placed at(0,0,0), and magnet 100 moves along the illustrated magnet path and hasa dipole moment in the y-direction in an embodiment. Sensor system 102is therefore shifted in the y-direction by yo and in the z-direction byz₀ with respect to the magnet path. In other embodiments, magnet 100 isstationary at (0,0,0) and sensor system 102 moves along a path.

In an embodiment, sensor system 102 comprises a plurality of at leasttwo sensor elements. A first sensor element detects the Bx-component andthe second sensor element, the Bz-component. Sensor system 102 computesa ratio of Bx/Bz, which is proportional to the x-position of the dipole.If magnet 100 is a perfect dipole, then x=z₀*(Bx/Bz).

If magnet 100 is not a perfect (spherical) dipole, x=f(Bx/Bz), wherein fis a non-linear function that can be expressed by a polynomial of asecond or higher order or by a look-up table in sensor system 102. Inpractice, spherical magnets can be used to obtain pure dipoles, butother magnet shapes can also be used, including cylinders, blocks andother suitable configurations. In embodiments, shapes that have small orvanishing octupole moments, which are good approximations of dipoles,can be chosen. For homogenous magnetization, the octupole momentvanishes for a specific aspect ratio of the magnet, e.g., length vs.diameter for cylindrical magnets. Higher magnetic multipoles arediscussed in Ausserlechner et al., “Pick-Up Systems for Vibrating SampleMagnetometers: A Theoretical Discussion Based on Magnetic MultipoleExpansions,” Meas. Sci. Technol. 5, 213-225, 1994, which is incorporatedherein by reference in its entirety.

In the aforementioned equations for x, it can be seen that the parameteryo is not a factor. Therefore, the system is robust against assemblytolerances in the y-direction. Moreover this means that the path doesnot necessarily have to be a straight-line parallel path to the x-axis,as depicted in FIG. 2; in embodiments, it can be an arbitrary curve in aplane z=z₀. In such embodiments, sensor 102 outputs the projection ofthe location onto the x-axis, i.e., the x-coordinate of the magnetlocation.

Additionally, embodiments can detect Bx and Bz individually and thencompute a ratio. This, for example, can be a useful methodology inembodiments in which sensor 102 comprises a Hall effect device.Additionally, the system can also detect a cosine signal, proportionalto Bx/sqrt(Bx²+Bz²) and a sine signal proportional to Bz/sqrt(Bx²+Bz²).The ratio of both can also be computed, as Bx/Bz. Sensor 102 cancomprise other sensor elements that directly detect Bx/Bz and/or Bz/Bxin embodiments. In other words, in various embodiments it is desired toobtain some signal proportional to Bx/Bz, and whether such a signalcomes from sensor 102 in some embodiments or results from on-chip signalprocessing in others is of little importance.

The system is also independent of the orientation of a substratesupporting sensor 102. It is possible to align a semiconductor die withits major surface parallel to the xy-plane. In this case, Bz is theout-of-plane component of the flux density, while Bx is one of the twoin-plane components. In an embodiment, Bz can be detected with aconventional Hall plate and Bx with a vertical Hall effect device.

In embodiments, a top surface of the sensor substrate can be parallel tothe xz-plane. In such an embodiment both Bx and Bz are in-planecomponents of the flux density. Both can then be detected with verticalHall effect devices arranged perpendicular with respect to each other,or with magnetoresistive (xMR) strips. For example, in one embodimentanisotropic magnetoresistive (AMR) strips with perpendicular currentflow directions are used, though giant MR (GMR) or other xMRtechnologies can be used in other embodiments.

Referring to FIG. 3A, simulation results for a spherical magnet having a10 mm diameter and 1 T remanence, magnetized in the y-direction, areshown. The magnet moves along a path parallel to the x-axis with y₀=10mm and z₀=10 mm (refer also to FIG. 2). Flux densities Bx and Bz aredepicted in FIG. 3A.

As can be seen, flux densities Bx and Bz without about +/−20 mm of thecenter are larger than 1 mT, which is easily detectable by variousmagnetic field sensors like xMRs and/or Hall effect devices. The ratioof the fields, depicted in FIG. 3B, is linear.

Assuming a zero-point error of the Bx sensor of Bx-offset=100 μT, theerror in the position estimation is then as depicted in FIG. 3C. Atabout x=+/−13 mm, the error in the x-estimation is −0.2 mm. at aboutx=+−/20 mm, the error is about −0.7 mm. If the x-position is kept fixed,e.g, at the large value of about +/−20 mm, and the zero-point error ofthe Bx sensor is changed, the error in the estimation of the x-positionis linear with respect to the zero-point error.

In other embodiments, lateral Hall plates alone can be used to implementa gradiometric system that is robust against homogeneous backgroundmagnetic fields. Referring to FIG. 4A, a sensor system 400 comprises atleast two sensor elements 402, such as Hall plates. Sensor elements 402are arranged on a substrate or semiconductor die 404. At least onesensor element detects the gradient dBz/dx associated with a magneticfield of a magnet 406 and at least one other sensor element detects thegradient dBz/dy. Sensor system 400 determines a ratio of(dBz/dx)/(dBz/dy), which is proportional to the x-position of magnet406. Sensor system 400 can detect the gradients individually anddetermine their ratio, or system 400 can detect Bz(x+del_x/2) andBz(x−del_x/2) and estimate dBz/dx≈(Bz(x+del_x/2)−Bz(x−del_x/2)/del_x,analogously for the y-direction. If magnet 406 is a perfect dipole, asdiscussed above, then x=y₀*(dBz/dx)/(dBz/dy).

As in other embodiments, perfect (i.e., spherical) magnets can be used,or other shapes can be used in other embodiments. If magnet 406 is aperfect dipole in the z-direction, then the gradients are as follows:

$\frac{\partial B_{z}}{\partial x} = {\frac{{- 3}B_{rem}V}{4\pi}x\frac{x^{2} + y_{0}^{2} - {4z_{0}^{2}}}{\left( {x^{2} + y_{0}^{2} + z_{0}^{2}} \right)^{2}}}$and$\frac{\partial B_{z}}{\partial y} = {\frac{{- 3}B_{rem}V}{4\; \pi}y_{0}{\frac{x^{2} + y_{0}^{2} - {4z_{0}^{2}}}{\left( {x^{2} + y_{0}^{2} + z_{0}^{2}} \right)^{7/2}}.}}$

It follows that:

${\frac{\partial B_{z}}{\partial x}/\frac{\partial B_{z}}{\partial y}} = {\frac{x}{y_{0}}.}$

In practice, sensor system can be challenged when magnet 406 passes thepoint:

2|z ₀|=√{square root over (x ² +y ₀ ²)}

Because both gradients vanish and a division-by-zero occurs in thefollowing equation:

$x = {y_{0}{\frac{\partial B_{z}}{\partial x}/{\frac{\partial B_{z}}{\partial y}.}}}$

In embodiments, therefore, 2*abs(z0)<abs(y0) is designed for, and z₀=0is chosen. Additionally, y₀, the distance between the x-axis and thepath of magnet 406, is as small as possible in embodiments in order tohave strong field gradients, the limits of which are given by therequirement that magnet 406 not collide with the sensor package ofsensor system 400.

Also similar to as previously discussed, even if magnet 406 is not aperfect dipole, then x=f((dBz/dx)/(dBz/dy)), where f is a nonlinearfunction that can be expressed by a polynomial of the second or higherorder or by a look-up table.

Similar to other embodiments discussed, the parameter z₀ does not enterthe aforementioned equation for x. Thus, these embodiments are alsorobust with respect to assembly tolerances, here in the z-direction.Additionally, the path need not be a straight line parallel to thex-axis, and the path could be an arbitrary curve in a y=y₀ plane.

As in other embodiments, system 400 is independent of substrate 404orientation. In FIG. 4A, a major surface of substrate 404 on whichsensor elements 402 are mounted is parallel with the xy-plane. Bz is theout-of-plane component of the flux density and can be detected withconventional lateral Hall plates. The gradient of Bz along the x-axis isdetected by two Hall plates placed along the x-axis, and the signals ofthese plates are then subtracted. The gradient of Bz along the y-axis isdetected by two Hall plates placed along the y-axis, with their signalssubtracted. It can be advantageous in such embodiments for the die orsubstrate 404 to be packaged in a sensor package having sensor leadspositioned on a single side of the package that opposes magnet 406.

In the embodiment of FIG. 4B, substrate 404 is oriented with the majorsurface on which sensor elements 402 are mounted being parallel to thexz-plane. In this embodiment, Bz is an in-plane component of the fluxdensity and can be detected with vertical Hall elements or withmagnetoresistive (xMR) strips, such as AMR, GMR or some othertechnology, as sensor elements 402. As depicted in FIG. 4B, sensorelements 402 are located at the same y-coordinate, and it is possible toderive the y-gradient from Maxwell's equation:

$\frac{\partial B_{z}}{\partial y} = {{- \frac{\partial B_{z}}{\partial x}} - {\frac{\partial B_{z}}{\partial z}\mspace{14mu} {with}}}$$\frac{\partial B_{z}}{\partial z} \approx {\frac{{B_{z}\left( {0,0,{\Delta/2}} \right)} - {B_{z}\left( {{0,0,} - {\Delta/2}} \right)}}{\Delta}\mspace{14mu} {and}}$$\frac{\partial B_{z}}{\partial x} \approx \frac{{B_{z}\left( {{\Delta/2},0,0} \right)} - {B_{z}\left( {{{- \Delta}/2},0,0} \right)}}{\Delta}$

Referring to FIG. 5A, simulation results for a spherical magnet having a10 mm diameter and 1 T remanence, magnetized in the z-direction, areshown. The magnet moves along a path parallel to the x-axis with y₀=5 mmand z₀=10 mm (refer also to FIGS. 2 and 4B). Gradients dBz/dx and dBz/dyare depicted in FIG. 5A.

As can be seen, both curves have zero-crossings at x=+/−about 0.02 m.The system in this embodiment can be operated in the region |x|<about 15mm, wherein the ratio of gradients is a linear function of thex-position, avoiding the zero-crossings.

Referring to FIG. 5B, simulation results for a spherical magnet with a20 mm diameter and 1 T remanence are depicted. The path of the magnet isin the x-direction with y0=13 mm and z0=0. The sensor elements arepositioned at (x,y,z)=(1.3 mm, 0, 0), (−1.3 mm, 0, 0), (0, 1.3 mm, 0)and (0, −1.3 mm, 0), and the gradient in the x-direction is approximatedby the subtraction of two opposing sensor elements. The differencebetween both sensor elements in the x- or y-direction is assumed to havea zero-point error of +/−25 μT, which leads to the errors in theestimation of the x-position as depicted in FIG. 5B.

For |x|<15 mm, the error is less than +/−0.2 mm and is mainly due to thefact that the gradient is approximated by the difference; as this is asystematic error, it can be improved by a nonlinear function thatoperates on the ratio of the gradients. At large |x|, different curvesoccur depending on the exact offset error of the sensor elements. Theseerrors in the estimation of x can be reduced in embodiments by usingstronger magnets, such as magnets with larger dipole moments and havinglarger remanence and/or volume, or by reducing the zero-point error ofthe sensor elements. A stroke of |x|<20 mm has errors within a band of+/−0.35 mm, and a stroke of 30 mm has errors within a band of +/−1.5 mm.

Embodiments can be made more accurate for small |x| by adding one ormore additional sensor elements 402 with smaller spacing on substrate404. For example, the aforementioned embodiment had two Hall platesarranged on the x-axis with a spacing of about 2.6 mm and two Hallplates arranged on the y-axis with a spacing of about 2.6 mm. Because ofthe relatively large spacing, the difference of two Hall plate signalsdoes not approximate the gradient very precisely and can have an errorof about +/−0.2 mm at x=+/−5 mm. An additional Hall plate on each of thex-axis and the y-axis with a spacing of about 0.6 mm provides that theirdifferences can be used to obtain a better approximation of thegradients.

It is also possible in embodiments to use only two additional sensorelements on the x-axis with about 0.6 mm of spacing and use the sensorswith 2.6 mm spacing on the y-axis to approximate the ratio of gradientsas follows:

${\frac{\partial B_{z}}{\partial x}/\frac{\partial B_{z}}{\partial y}} \approx {\frac{{B_{z}\left( {0.3\mspace{14mu} {mm},0,0} \right)} - {B_{z}\left( {{- 0.3}\mspace{14mu} {mm},0,0} \right)}}{0.6\mspace{14mu} {mm}} \times \frac{2.6\mspace{14mu} {mm}}{{B_{z}\left( {0,1.3\mspace{14mu} {mm},0} \right)} - {B_{z}\left( {{0,} - {1.3\mspace{14mu} {mm},0}} \right)}}}$

Embodiments can also be made suitable for extended measurement ranges.This can be done, for example, by detecting the minima and maxima of theBz field. In one embodiment, and referring to the sensor system 600 ofFIG. 6A, vertical Hall elements 602 and 604 are used as switches foreither Bx (602) or By (604). Sensor elements 602 and 604 sense theminima and maxima in the out-of-plane component Bz sensed by lateralHall element 606. Use of vertical Hall elements 602 and 604 as switchescan extend the range of lateral Hall element 606, and elements 602 and604 can be optimized for a very small measurement range because only theswitching limit is covered by vertical Hall elements 602 and 604.Lateral Hall element 606, sensing the out-of-plane Bz component, can bedesigned for a much larger measurement range in embodiments.

By determining the minima and maxima of Bz, with reference to theembodiment of FIG. 6A, sensor system 600 can determine which linearrange the signal is within in order to determine which of three look-uptables 608 to use for a linearization algorithm. A first look-up table608 a is associated with a sensor range less than the minima of Bz, asecond 608 b with a range between the minima and maxima and a third 608c with a range above the maxima.

In another embodiment, and referring to FIG. 6B, a differentialarrangement can be used to calculate the gradient of Bz. The gradientcan be used for the detection of the local minima and serves a switchbetween three different linearization tables 608 a-c. All of sensorelements 602, 604 and 606 can be lateral Hall elements in such anembodiment.

Embodiments also relate to detecting the position of an element thatmoves in three-dimensional space. These embodiments rely on the theorythat location estimation works better with increased distance; in otherwords, the position sensor favors far-field approximation of the fieldover near-field contributions. The far-field is the dipole part of thefield, whereas the near-field includes higher multipole parts. Thissuggests that an ideal magnet is a pure dipole with verticalmagnetization.

As previously mentioned, the simplest way to obtain a dipole is by ausing a spherically-shaped magnet. If a perfect dipole magnet is used,the magnetic field is:

Bx=Brem*Volume/(4*Pi*r{circumflex over ( )}5)*3*x*z

By=Brem*Volume/(4*Pi*r{circumflex over ( )}5)*3*y*z

Bz=Brem*Volume/(4*Pi*r{circumflex over ( )}5)*(2*z{circumflex over( )}2−x{circumflex over ( )}2−y{circumflex over ( )}2)

where r=sqrt(x{circumflex over ( )}2+y{circumflex over( )}2+z{circumflex over ( )}2), which is a nonlinear function of x, yand z; x=y=z=0 in the center of the magnet, Brem is the remanence of themagnet, and Volume is the volume of the magnet. Thus, there are threeequations for three unknowns (x,y,z) if Brem*Volume is assumed to beknown. The positions can be obtained by solving the set of equations,which can be done in myriad ways.

The system can thus determine not just a single coordinate but all threex, y and z coordinates. Moreover, the system is not plagued byinaccuracies close to the magnet, as in conventional solutions, becausethe magnetic field has no higher order multi-pole contributions. Thefield has only a dipole no matter how large the distance between themagnet and sensor.

Movement of the magnet can be in x- or y-direction or within planesparallel to the xy-plane. Movement can include z-contributions, thus thedirection of magnetization does not need to be perpendicular to themovement, as in conventional solutions.

The sensor for three-dimensional embodiments is desired to be highlylinear over a wide dynamic range. Therefore, xMR elements and magneticconcentrators are generally not suitable. Hall devices, however, can beused, with lateral Hall elements measuring the magnetic field componentperpendicular to the die surface and vertical hall devices measuring thein-plane field components. It is also possible in embodiments to uselateral Hall plates in combination with soft magnetic components, suchas spheres.

In practice, the magnetic field decreases when the moving magnet isfarther away from the sensor, i.e., at maximum stroke of the movement.The system can therefore be vulnerable to interference from externalmagnetic fields, such as electromagnetic interference (EMI), the earth'sfield or other electromechanical equipment, and shielding can beimplemented in embodiments.

Referring to FIG. 7A, a hemispherical magnet 702 is mounted on a surfaceof a panel 704 spaced apart from a sensor 706. In embodiments, panel 704can comprise a soft magnetic material, such as iron, steel or some othersuitable material and is highly permeable, e.g., μ>>1. As such, panel704 acts as a magnetic mirror, mirroring the half-sphere magnet 702 toform a complete sphere. Thus, the relatively more expensive material ofmagnet 702 is saved while maintaining the same strength of the magneticfield on sensor 706, and panel 704 shields magnet 702 and sensor 706from external magnetic disturbances.

In embodiments, panel 704 and magnet 702 are firmly coupled such thatpanel 704 moves with the body having a position to be detected. In otherembodiments, panel 704 can be stationary, with magnet 702 movingrelative to panel 704. A small gap exists between panel 704 and magnet702 in these embodiments to enable magnet 702 to move.

While panel 704 is depicted as a flat or rectangular structure, it canhave other shapes in various embodiments, such as arced, a hollowcylinder or any curves surface, among others. It can be advantageous inembodiments for the distance between magnet 702 and panel 704 to remainconstant during movement of magnet 702. Embodiments can also comprisemultiple panels 704, as depicted in FIGS. 7B and 7C, which createinfinite numbers of dipoles given the minoring effects of the opposingpanels 704.

The shape and configuration of magnet 702 can also vary. In general,magnet 702 has negligible higher multipoles; in other words, magnet 702can be shaped to make the octupole vanish, which can be accomplished inembodiments by forming a hole or recess in a cylindrical magnet.

Various embodiments of systems, devices and methods have been describedherein. These embodiments are given only by way of example and are notintended to limit the scope of the invention. It should be appreciated,moreover, that the various features of the embodiments that have beendescribed may be combined in various ways to produce numerous additionalembodiments. Moreover, while various materials, dimensions, shapes,configurations and locations, etc. have been described for use withdisclosed embodiments, others besides those disclosed may be utilizedwithout exceeding the scope of the invention.

Persons of ordinary skill in the relevant arts will recognize that theinvention may comprise fewer features than illustrated in any individualembodiment described above. The embodiments described herein are notmeant to be an exhaustive presentation of the ways in which the variousfeatures of the invention may be combined. Accordingly, the embodimentsare not mutually exclusive combinations of features; rather, theinvention may comprise a combination of different individual featuresselected from different individual embodiments, as understood by personsof ordinary skill in the art.

Any incorporation by reference of documents above is limited such thatno subject matter is incorporated that is contrary to the explicitdisclosure herein. Any incorporation by reference of documents above isfurther limited such that no claims included in the documents areincorporated by reference herein. Any incorporation by reference ofdocuments above is yet further limited such that any definitionsprovided in the documents are not incorporated by reference hereinunless expressly included herein.

For purposes of interpreting the claims for the present invention, it isexpressly intended that the provisions of Section 112, sixth paragraphof 35 U.S.C. are not to be invoked unless the specific terms “means for”or “step for” are recited in a claim.

1-4. (canceled)
 5. A method of sensing a linear position of an objectcomprising: coupling one of a permanent magnet or a sensor to theobject, the permanent magnet being magnetized in a z-direction;arranging the other of the sensor or the permanent magnet proximate toand spaced apart from the one of the permanent magnet or the sensor in ay-direction; sensing a change in an x-direction of a magnetic fieldcomponent Bz of the permanent magnet by a first sensor element of thesensor; sensing a change in the y-direction of the magnetic fieldcomponent Bz of the permanent magnet by a second sensor element of thesensor; determining a ratio of dBz/dx to dBz/dy; and determining aposition of the object on the path from the ratio.
 6. A method ofsensing a linear position of an object comprising: coupling one of apermanent magnet or a sensor to the object, the permanent magnet beingmagnetized in a y-direction; arranging the other of the a sensor or thepermanent magnet proximate to and spaced apart from the one of thepermanent magnet or the sensor in a y-direction and a z-direction;sensing a Bx component of a magnetic field of the permanent magnet by afirst sensor element of the sensor; sensing a Bz component of themagnetic field of the permanent magnet by a second sensor element of thesensor; determining a nonlinear function of Bx and Bz; and determining aposition of the object on the path from the nonlinear function. 7-13.(canceled)